Prime Numbers Wiki:Divisibility Rules Sandbox 2
For explanation of general divisibility rules explained, see Divisibility Rules. Below is a List of Divisibility Rules sorted by number. Difficulty Coding Divisibility of Numbers below 10 |simpex=4,623 is divisible by one; 91,237 is divisible by one. }} |simpex=65,156,151,594 is divisible by two because the units digit is 4, and 1,597,534,568,852 is divisible by two because the units digit is 2. }} |simpex=Is 12423 divisible by 3? #Add all the digits together, we get 1 + 2 + 4 + 2 + 3 = 12. #12 is divisible by 3, so 12423 is, too. }} |simpex=156,128 is divisible by four, and 6,416 is divisible by four. The last two digits are 28 and 16, respectively, both of which are divisible by 4. }} |simpex=213,478,765 is divisible by 5 because the last digit is 5. }} Another strategy is to add 5 times the last digit to the remaining digits instead. |simpex=Is 3,409 is divisible by 7? First, take 9 from 3409, and multiply 9 by 2 (9*2=18). Then, subtract the doubled digit to the remaining digits. (340-18=322) Repeat the process: take 2 from 322 and multiply it by 2 (2*2=4). Subtract the doubled digit to the remaining number (32-4 28) 28 is divisible by 7, so |adv=Sort the numbers in blocks of three from right to left. Then, add the first group from the right, subtract the second group, then add the third, subtract the fourth, and so on. This is called the alternating sum of three. If the result is the multiple of 7, then the number is divisible by 7. |advex=Is 1,702,906,247 divisible by 7? First, group the numbers into blocks of three: 247, 906, 702, 1. Then, form the alternating sum: 247 - 906 + 702 - 1 = 42 Examine the results. Since 42 = 7 * 6, 42 is divisible by 7, thus 1,702,906,247 is, too. }} |simpex=Is 14625 divisible by 9? #Add all the digits together: 1 + 4 + 6 + 2 + 5 = 18 #18 is divisible by 9, so 14625 is, too.}} Divisibility of Numbers between 11 and 20 }} 56 is divisible by 7. Therefore, }} Divisibility of Numbers between 21 and 30 As 73,857 is divisible by both 3 and 7, 73,857 is divisible by 21. |adv=Alternatively, take the last digit of the number, multiply it by two, and then subtract it from the remaining digits of the numbers. Repeat the process until the result can be easily identified. |advex=To be filled up }} , so 33,242 is divisible by 22. }} 52 is divisible by 13. Therefore, }} 35 is divisible by 7. Therefore, }} Divisibility of Numbers between 31 and 40 Divisibility of Numbers between 41 and 50 Divisibility of Numbers between 51 and 60 Divisibility of Numbers between 61 and 70 Divisibility of Numbers between 71 and 80 Divisibility of Numbers between 81 and 90 Divisibility of Numbers between 91 and 100 |} Techinical Divisibility of Number Information Below lists down all the possible methods. The methods recommended will be '''bolded' and displayed in blue text. Prime numbers from 2 ~ 100 |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= }} |trim3= |trimleft=3 (multiply the first digit by 3, and then shift it 2 digits to the right, and add.)}} Prime numbers from 101 ~ 200 |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= }} |trim2= |trim3= |trimleft=3 (multiply the first digit by 3, and then shift it 2 digits to the right, and add.)}} Prime numbers from 201 ~ 300 Prime numbers from 301 ~ 400 Prime numbers from 401 ~ 500 Prime numbers from 501 ~ 600 Prime numbers from 601 ~ 700 |trim2= }} RemoveWikiaRail